Helmholtz 3D
This is the most geometrically complex example in the tutorial set: a 3D Helmholtz problem on an extruded letter-F style geometry.
Problem Setup
The script works with mixed boundary conditions on a 3D domain and compares VPINN and FEM-style weak-form ideas on a nontrivial mesh.
Step 1: Build a Custom 3D Geometry
A custom geometry constructor creates the volume and tagged surfaces required for boundary conditions.
Step 2: Assemble Weak-Form Quantities in 3D
The example uses tetrahedral-style weak-form machinery rather than a pointwise PDE residual.
Step 3: Visualize the 3D Result
The script includes a surface or boundary visualization pipeline so the final field can be interpreted geometrically.
What To Notice
- This is a high-end tutorial example rather than a first learning example.
- Complex geometry handling is one of the main reasons weak-form approaches become valuable.
- The workflow shows how jNO scales beyond unit-interval and unit-square toy problems.